I think people, in general, get too dramatic about oppositions. I am a Cancer Sun with a Capricorn Moon, and I do tend to hold my emotions in too much. Watch out for that, it can make you physically sick if your life is going through a very stressful stage. But being a Cancer Sun, you aren't cold enough that those you care about don't know how much you love them. Capricorn isn't really detached, it's sort of discriminating, in the sense that you decide if it's worth it for you to get involved in too many emotional stimuli if it's silly or doesn't serve your life or help your family or loved ones in some way. Capricorn Moon is reserved, shows their feelings more in private, but cares deeply.
The way you say "process and react" suggests to me that's your Virgo Rising speaking. This is a very analytical sign, and the Rising sign is how others see you. You have an active mind, come off as an intellectual. But Virgo can be critical, so couple that with the reserve of a Capricorn Moon, and that's what the issue is. But all three parts of this Trinity are equal, and you have seven other planets all in zodiac signs too. Try to focus more on your Cancer Sun and be expressive. Both Cancer and Virgo are chatty signs who love to talk. That should be a way to open up more. Now, I'm not sure why so many emotional stimuli are always in your life, I can't tell from the Trinity. Try not to overthink things when it comes to emotions (I know, easier said than done). And the reserve and thoughtful attitude should be used to weed out some drama that you really don't need to get involved in. Sometimes we need to take some people in smaller doses :).